Recycling of strange sets: I. Cycle expansions
- 1 May 1990
- journal article
- research article
- Published by IOP Publishing in Nonlinearity
- Vol. 3 (2), 325-359
- https://doi.org/10.1088/0951-7715/3/2/005
Abstract
The strange sets which arise in deterministic low-dimensional dynamical systems are analysed in terms of (unstable) cycles and their eigenvalues. The general formalism of cycle expansions is introduced and its convergence discussed.Keywords
This publication has 41 references indexed in Scilit:
- On the mode-locking universality for critical circle mapsNonlinearity, 1990
- Periodic-orbit quantization of chaotic systemsPhysical Review Letters, 1989
- Scaling properties of multifractals as an eigenvalue problemPhysical Review A, 1989
- Invariant Measurement of Strange Sets in Terms of CyclesPhysical Review Letters, 1988
- Locating resonances for AxiomA dynamical systemsJournal of Statistical Physics, 1986
- Escape from strange repellersProceedings of the National Academy of Sciences, 1984
- An Analogue of the Prime Number Theorem for Closed Orbits of Axiom a FlowsAnnals of Mathematics, 1983
- Chaos, External Noise and Fredholm TheoryProgress of Theoretical Physics, 1980
- GIBBS MEASURES IN ERGODIC THEORYRussian Mathematical Surveys, 1972
- Differentiable dynamical systemsBulletin of the American Mathematical Society, 1967